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不动点集为P(2m,2l+1)∪P(2m,2n+1)的对合 被引量:9

Involutions with Fixed Point Set P(2m,2l+1)∪P(2m,2n+1)
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摘要 设(M,T)是一个带有光滑对合T的光滑闭流形,T在M上的不动点集为F={x|T(x)=x,x∈M},则F为M的闭子流形的不交并.本文证明了:当F=P(2m,2l+1)■P(2m,2n+1)时,其中n>l■m,m≠1,3,(M,T)协边于零. Let (M, T) be a smooth closed manifold with a smooth involution T whose fixed point set is F = {x|T(x) = x, x ∈ M}, then F is the disjoint union of smooth closed submanifold of M. In this paper, we discuss: for F=P(2m,2l+1)∪P(2m,2n+1), n 〉 l≥m,m≠ 1, 3, then (M, T) is bounded.
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 2008年第5期971-978,共8页 Acta Mathematica Sinica:Chinese Series
基金 国家自然科学基金(10371029) 河北省自然科学基金(103144) 教育厅博士基金资助项目(201006)
关键词 对合 不动点集 示性类 协边类 involution fixed point set characteristic class cobordism class
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参考文献7

  • 1Conner P. E., Differentiable periodic maps (2nd ed), Lecture Notes in Math., 738, Berlin and New York: Spring, 1979.
  • 2Wu Z. D., Involutions fixing Dold manifold P(2m, 2n), Acta Mathematica Sinica, Chinese Series, 1988, 31(1): 72-82.
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  • 7Stong R. E., Vector bundles over Dold manifolds, Fundamenta Mathematicae, 2001, 169: 85-95.

同被引文献38

  • 1李日成,马凯,吴振德.RP(j)×CP(k)上向量丛的全Stiefel-Whitney类[J].数学学报(中文版),2007,50(3):535-538. 被引量:4
  • 2Conner P E.Differentiable Periodic Maps[M].Lecture Notes in Math.2nd ed.Berlin:Springer,1979:738.
  • 3Stong R E.Involutions Fixing the Projective Spaces[J].Michigan Math J,1966,13(4):445-447.
  • 4Royster D C.Involutions Fixing the Disjoint Union of Two Projective Spaces[J].Indiana Univ Math J,1980,29:267-276.
  • 5L(U) Zhi,LIU Xi-bo.Involutions Fixing the Disjoint Union of 3-Real Projective Space with Dold Manifold[J].Kodai Math J,2000,23(2):187-213.
  • 6Kosniowski C,Stong R E.Involutions and Characteristic Numbers[J].Topology,1978,17(4):309-330.
  • 7Fujii M,Yasui T.KO-Cohomologies of Dold Manifold[J].Math J Okayama Univ,1973,16(1):55-84.
  • 8Stong R E.Vector Bundles over Dold Manifolds[J].Fundamenta Mathematicae,2001,169(1):85-95.
  • 9吴振德.不动点集为Dold流形P(2m,2n)的带有对合的流形[J].数学学报,1988,31(1):72-82.
  • 10CONNER P E. Differentiable Periodic Maps,Lecture Notes in Math [M] Berlin:Spring, 1979:738.

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